A Brief History of Volatility Models

Monte Carlo Simulation GBM (drift=1%,sigma=20%,T=1,M=1000,dt=1/500)
  1. European options can only be exercised at expiration.
  2. Risk-Free asset — there is a risk-free asset that we can borrow and invest our cash in(zero-coupon bond).
  3. Absence of dividend/accrued interest throughout the lifetime of the option.
  4. There are no transaction costs when buying/selling options, and delta hedging.
  5. The underlying asset follows a continuous BM, and returns are normally distributed (the model cannot handle jumps and discontinuity in asset price dynamic).
  6. Volatility is constant across all strikes and maturities.

The Era of Stochastic Volatility

Interest Rates

Foreign Exchange

Equities/Commodities

Looking forward into the future — Rough Volatility

So what has changed over the last few decades that makes practitioners think that volatility is rough?

Rough Volatility applications

  1. Estimating volatility regime using the Hurst index — As we know by now, the Hurst index is a measure of the time-series autocorrelation. Empirical studies have shown that this index stays relatively stable at a very low level most times (Gatheral et. al found that for equity indices H=0.13 on long term horizon), this means that volatility exhibits in normal markets strong mean reversion. Historically speaking, during periods of financial stress that index tends to rise significantly, therefore, we can use that indicator as a signal of change in the volatility regime.
Credit — Rough Volatility: An overview. Jim Gatheral

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Harel Jacobson

Harel Jacobson

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Global Volatility Trading. Python addict. Bloomberg Junkie. Amateur Boxer and boxing coach (RSB cert.)!No investment advice!